# Relation between Change in Potential Energy and Work Done

1. Jun 22, 2013

### andyrk

Why is dU=-$\vec{F}$.d$\vec{r}$
Integrating with putting the limits on we get:
ΔU=-W
Why is this? Here $\vec{F}$ is a conservative force/Force field.

2. Jun 22, 2013

### tiny-tim

3. Jun 22, 2013

### andyrk

Does it have any proof? Or is it just stated out of nowhere?

4. Jun 22, 2013

### dreamLord

Potential Energy is actually defined that way. It doesn't require a proof.

5. Jun 22, 2013

### tiny-tim

yup!

definition!

(also applies eg to gravity)

(and only works for conservative forces)